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FRM Part I · FRM Exam Part I · Option Sensitivity Measures: The "Greeks"

A portfolio has delta of 2,000, gamma of 100 per $1, vega of 15,000 per 1 volatility point (1%), and theta of -3,000 per day. Over one day the stock rises by $2, implied volatility falls by 0.5 point, and the time effect applies for one day. What is the estimated change in portfolio value using delta, gamma, vega and theta?

The estimated change is a loss of $6,300. Delta adds $4,000, gamma adds $200, the volatility drop subtracts $7,500, and one day of theta subtracts $3,000, for a net of negative $6,300.

  1. A-$6,300Correct
  2. B-$3,000
  3. C$300
  4. D-$6,000

Explanation

Delta: 2,000 x 2 = 4,000. Gamma: 0.5 x 100 x 4 = 200. Vega: 15,000 x (-0.5) = -7,500. Theta: -3,000. Sum = 4,000 + 200 - 7,500 - 3,000 = -6,300. The -$6,000 option omits gamma and the $300 option omits theta... it equals 4,000+200-3,900 style errors and is wrong.

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